Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9445)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.9445.01

Input Form

HypergeometricPFQ[{-(19/4)}, {3/2, -(13/4)}, -z] == (1/(122174325 Sqrt[2])) (z^(1/4) ((122174325 - 262004400 z + 111525120 z^2 - 25128960 z^3 + 6619136 z^4 + 524288 z^5) BesselJ[-(1/4), Sqrt[z]]^2 - 16 Sqrt[z] (-11533725 + 4132800 z - 887040 z^2 + 196608 z^3 + 16384 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (228118275 - 302112720 z + 119427840 z^2 - 26578944 z^3 + 6488064 z^4 + 524288 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]